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On upper and lower values of a generalized function at a point

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Abstract

In this paper we introduce, for generalized functions of D′(R1), the concepts of functions of upper and lower values, and we give a complete description of them for generalized functions belonging locally to∞.

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Literature cited

  1. Ya. Mikusinskii and R. Sikorskii, Elementary Theory of Generalized Functions [in Russian], Moscow (1959).

  2. I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Moscow (1957).

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Authors and Affiliations

  1. Voronezh State University, USSR

    Yu. P. Chuburin

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  1. Yu. P. Chuburin
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Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 339–348, September, 1973.

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Chuburin, Y.P. On upper and lower values of a generalized function at a point. Mathematical Notes of the Academy of Sciences of the USSR 14, 755–760 (1973). https://doi.org/10.1007/BF01147450

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  • DOI: https://doi.org/10.1007/BF01147450

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